In the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.
In trigonometry, for a right triangle, the sine (sin) of any angle θ is given as the ratio of its opposite side to the hypotenuse of the triangle, that is, sin θ = (opposite side)/(hypotenuse).
In the question, we are asked to find the trigonometric ratio, sin J, for the given right triangle JKL.
The side opposite to angle J is KL, which has a value of 3 units.
The hypotenuse of the given right triangle is JK, which has a value of 7.8 units.
Thus, sin J can be calculated as:
sin J = KL/JK = 3/7.8 = 5/13 = 0.39.
Thus, in the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.
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